Greedy orthogonal matching pursuit for subspace clustering to improve graph connectivity

Subspace clustering methods based on self-expressiveness model have recently attracted much attention. However, there exists a gap between subspace-preserving coefficient and the final clustering result due to the lack of graph connectivity. The problem has not been well tackled in the published literature. This paper significantly improves the graph connectivity by adding an effective projection step to the recently proposed method SSC-OMP. With this projection step, it is possible to establish a theoretical guarantee that the subspace-preserving condition leads directly to the exact clustering result, which bridges the gap. Moreover, the potential advantage of the proposed algorithm over prior methods is its robustness to noise. Experimental results demonstrate that the proposed approach enjoys a high clustering accuracy and a fast processing speed in comparison with state-of-the-art algorithms.